Abstract

In Structuralism Piaget provides an overlook on the penetration of the idea of “structure” in various fields of natural and social sciences. Through the different applications and contributions exemplified in the book, structuralism appears as a powerful approach to the analysis of phenomena in several fields of knowledge.

Rather than looking at the structure as a given order that exists in reality, Piaget advises that it is more useful to consider it a sort of approach, a method of examination of reality, which has certain rules and implications. In this sense, structure is an a priori, the condition to detect in things regularity and discontinuity, connections and differences.

The three main characters of the structuralist approach are:

structures are based on the idea of wholeness. Structuralism objects to the atomism of the analytical and empiricist perspectives, and thus the vision of the theoretical work as taking apart or putting together isolated elements.

structures are systems characterizes by specific dynamics of transformations, through which they develop and change, while keeping certain boundaries.

structures are self-regulating: structures change according to their own rules, without the need for an external intervention

Structuralism could be considered the most systematic and methodical approach to the understanding of social and natural phenomena. It entails the study of phenomena through hypothetical models or “structures”, with a special focus on the study of the laws that govern such structures. A structure is thus a hypothetical, heuristic model used for the relational investigation of phenomena.

As a method, structuralism replaces the atomistic emphasis on phenomena seen as unique and mutually independent entities, by elaborating hypothetical models of a more general order with the goal of shifting the emphasis to the relationship between these phenomena.

In social science for example, structuralism, by emphasizing systems of relationships, aims at de-emphasizing the role of the subject, while emphasizing the structured character of the human condition, with its built-in constraints and patterns.

In its ambition to be systematic, structuralism borrows from any scientific domain in which the phenomena observed have been organized into a grammar of forms and structural relationships.

Introduction

Structuralism is hard to define because it has taken many different forms. When introducing its general traits, we encounter two main problems:

to define the nature of ideal of the concept of structure

to observe the critical intentions which accompanied the birth of any variety of structuralism

The idea of structure: there is an ideal of intelligibility held in common by all structuralists (mathematics, linguistics, psychology, philosophy, etc.) If we should focus on the positive content of the idea of structure, we could come upon at least two aspects are common to all kinds of structuralisms:

structures are self-sufficient, we do not have to make reference to all sorts of extraneous elements to understand them;

their theoretical employment has shown that structures, despite their diversity, have certain common properties; (p.4)

Three main characteristics of structures: “ In short the notion of structure is comprised of three key ideas: the ideas of wholeness, the idea of transformation, the idea of self-regulation” (p.5)

Structures involve transformations regulated by laws: “ We may say that a structure is a system of transformations. Inasmuch as it is a system and not a mere collection of elements and their properties, these transformations involve laws.” (p.5)

Structures have distinct characteristic in different scientific domains: “The mode of existence of a structure must be determined separately for each particular area of investigation” (p.5)

Wholeness

Structures vs aggregates: “All structuralists recognize as fundamental the contrast between structures and aggregates, the former being wholes, the latter composites formed of elements that are independent of the complexes into which they enter” (p.7)

Structures do have elements, but the “elements of a structure are subordinated to laws, and it is in terms of these laws that the structure qua whole or system is defined (…) These laws confer on the whole as such overall properties distinct from the properties of its elements” (p.7)

The idea of wholeness raises two main problems:

nature of wholeness: it would be a mistake to consider wholes either in terms of their structural laws or allow only for atomistic compounding of prior elements. There is a third position, which is that if operational structuralism: the logical procedures or natural processes by which the whole is formed are primary, not the whole, which is consequent on the system’s laws of composition, or the elements. (p.9).

formation of wholeness: have these composite wholes always been composed? Do structures call for formation, or is only some sort of eternal preformation compatible with them? (p.9) These questions lead us to the second characteristic of structures, namely their being systems of transformations, rather than of static forms.

Transformations

The laws governing structures are themselves structuring: it is the constant duality of being simultaneously structuring and structured that account for the success of the notion of law or rule employed by structuralists (p.10).

Structuralism started with the work of Saussure and it is associated with the work of Gestalt psychologists. Linguistics and psychological structuralism were associated with the dawning of ideas of transformation (p.11)

All known structures are, without exception, systems of transformation. (p.11)

Self-regulation

Self-regulation entails self-maintenance and closure: transformations inherent in a structure never lead beyond the system but always engender elements that belong to it and preserve its laws. In this sense the structure is closed.

These properties of conservation along with stability of boundaries despite the construction of indefinitely many new elements presuppose that structures are self-regulating. (p.11)

How is self-regulation achieved? At the highest level self-regulation proceeds by application of perfectly explicit rules, these rules being, of course, the very ones that define the structure under consideration, for examples operations. But what’s is an operation structurally considered? It is a perfect regulation, which has its inverse in the system. (p.15)

There is a vast class of structures which are not strictly logical or mathematical, that is, whose transformations unfold in time (linguistic, sociological, psychological structures). Such transformations are governed by laws that are not operations in the strict sense of the word, but they depend on the interplay of anticipation and correction. (p.16)

Rhythm, regulation, operation, these are the three basic mechanisms of self-regulation and self-maintenance. (p.16)

2 Mathematical and Logical Structures

Structuralists concepts derive from general algebra. The first known structure was the mathematical “group”: a group is a system consisting of a set if elements together with an operation of rule of combination and having the following properties:

performed upon elements of the set, the combinatory operation yields only elements of the set

the set contains a neuter element which doesn’t affect the combinatory operation with any other member of the group

the combinatory operation has an inverse in the system (+n – n = 0)

the combinatory operation is associative

The primary reason for the success of the group concept is the peculiar form of abstraction by which it is obtained, named “reflective abstraction”: it does not derive properties from things but from our ways of acting on things, the operations we perform on them. (p.19)

Groups also obey the rules of transformations and self-regulation (p.20)

“Parent structures”

The Bourbaki wanted to subordinate all mathematics to the idea of structure, thus overcoming the traditional compartmentalization. The group structure is quite independent of the intrinsic nature of its elements, and the transformations are disengaged from the object subject of such transformation

The Bourbaki program consists essentially in extending this procedure by subjecting mathematical elements of every variety, regardless to of the standard mathematical domain they belong, to this sort of “reflective abstraction” so as too arrive at structures of maximum generality. (p.24)

Three kinds of parents structures: algebraic, order and topologic, organized by two methods of constructions, combination and differentiation (p.25)

Does this mathematical architecture build on foundations that are in some manner natural, or are the Bourbaki parent structures simply an axiomatic basis of their system? From the study of the intellectual development of the child it seems that “the mother structures of the Borurbaki correspond to coordinations that are necessary to all intellectual activity. (p.27).

Logical structures

Logic systems have all the characteristics of structure (see p.29) but are lacking in two respects: “they are fabricated ad hoc, and structuralism is really after is the discovery of the “natural structures”; also, a logical system is only a relative whole, since it is open “at the top” (formulae that are indemonstrable so long as one stays in the system), and “at the bottom”, since primitive conceptions and axioms have all sorts of implicit elements.

Godel: no consistent formal system sufficiently “rich” to contain elementary arithmetic can, by its own principles of reasoning, demonstrate its own consistency. This undermined the formalist idea that mathematic was reducible to logic and logic could be exhaustively formalized. Since Godel we know that axiomatic method has certain inherent limitations.(p.33)

This had the effect of creating the notion of “weak” and “strong” structures. This hierarchy gave rise to an idea of “construction”, just as in biology the hierarchy of properties suggested the idea of “evolution”. (..) The idea of structure as a system of transformations becomes continuous with that of construction as a continual formation. (p.34)

3 Physical and biological structures

Is man, nature, or both the source of structure? In the terrain of physics they come together (p.37)

The harmony between mathematics and physics (..) is a correspondence of human operations with those of object-operators, a harmony, then, between the human being and the innumerable operators in nature. (p. 41)

Organic strucures

The organism is the paradigm structure. However, biological structuralism is only in its beginnings. Reductionist approaches in biology failed to see that never in physics progress takes the form of simply adding on new information (p.45)

The first attempt to introduce an explicitly structuralist perspective into biology was inspired by work in experimental psychology concerned with perceptual or motor schemes (Gestalten)

The notion of structure as a self-regulationg system should be carried beyond the individual organism, even beyond the population, to encompass the complex of milieu, phenotype and genetic pool. (..) Biological wholes and self-regulating systems enable us to understand the connection between “structures” and “ the subject” (p.51)

4 Psychological structures

The most prominent form of psychological structuralism is the theory of Gestalten. The central idea of Gestaltist structuralism is the idea of wholeness: complex perceptual units like a melody of a person’s physiognomy have perceptual qualities accrue to them as configurations (Gestalten). Gestalt psychologists maintained that what is given is always from the start a whole, a structure within which the sensations figure only as elements (p.56)

Laws of perceptual totalities:

the whole, over and beyond having qualitative features of its own, has a quantitative value different from that of the sum of its parts.

Perceptual totalities tend to take on the “best” form possible, “good” forms being simple, regular, symmetrical, closely packed, and so on. This entails physical principle of equilibration. (p.56)

The notion of equilibration is important, because it involves the idea of transformation within a system and the idea of self-regulation. Gestalt psychology is therefore a structuralist theory more on account of its use of equilibration principles than because of the laws of wholeness it proposes. (p.57)

5 Linguistic Structuralism

Language is a group institution. The syntax and semantics of a language yield a set of rules to which any individual speaking that language must submit. It is the natural source of structures. (p.75)

Linguistic structuralism goes back to Saussure, who showed that diachronic development is not the only process to be taken notice of in the study of a language. In addition to its historical aspect language has a “systematic” aspect; it embodies laws of equilibrium which operate on its elements and which yield a synchronic system. (p.76)

Fundamental importance of the arbitrariness of the verbal sign, which is merely conventional.

The relations between synchronics and diachronics must be different in linguistics than in other domains, where structure belongs not to the means of the expression, but to the expressed, to the signified rather than to the signifier, to realities which have intrinsic value and normative power. (p. 79)

Transformational structuralism

Chomsky’s theories place linguistic structures among those maximally general structures which derive their wholeness not from descriptive and static laws but from laws of transformation. (p.81)

Two key ideas of Chomsky’s linguistics: generative grammar, and the placement of this grammar in an innate reason. (p.82)

Applications of Chomsky’s structuralism are noteworthy for several reasons. First, they do much to attenuate the contrast between language as a social institution and speech as an individual performance, and to cast doubt upon the notion that the development of speech and with it of all individuals consists merely in an adaptation of the collective norms (p.85)

6 Structural analysis in the social sciences

All the social sciences yield structuralist theories since, however different they may be, they are all concerned with social groups and subgroups, that is, with self-regulating transformational totalities. A social group is evidently a whole; being dynamic, it is the seat of transformations; and since one of the basic facts about such groups is that they impose all sorts of constraints and norms, they are self-regulating. (p.97)

Analytic structuralism: Marcel Mauss is considered the originator of authentic anthropological structuralism because, especially in his studies on the gift, he sought and found the details of transformational interactions. (p.98)

Anthropological structuralism of Levi-Strauss

Fundamental principle of his structuralism: “all social life, however elementary, presupposes an intellectual activity in man of which the formal properties cannot, accordingly, be a reflection of the concrete organization of society” (p.107)

Anthropological structuralism is firmly synchronic, but in a different way than with linguistics. The system of beliefs and customs studied by the anthropologists is less subject to change than the language systems studied by the linguist. (..) The norms themselves depend upon structures, which are permanent, so that this sort of synchronics is somehow expression of an invariant diachronics. This does not mean that Levi-Strauss wants to abolish history; only, the changes brought about by history do not affect the human mind itself and, furthermore, their analysis again requires recourse to “structures” – diachronic instead of synchronic. (107)

Concept of pre-logic: pre-logic in the double sense of being anterior to an explicit logic and of being preparatory for the latter. (p.116)

Whereas other animals cannot alter themselves except by changing their species, man can transform himself by transforming the world can structure himself by constructing structures; and these structures are his own, for they are eternally predestined. So the history of intelligence is not simply an inventory of elements; it’s a bundle of transformations, not to be confused with the transformations of culture or those of symbolic activity, but antedating and giving rise to both of these. (p.119)

7 Structuralism and philosophy

Structuralism and dialectic

Levi Strauss discussed Sartre’s Critique of the Dialectic Reason: Piaget says that “ in the domain of the sciences themselves structuralism has always been linked with a constructivism from which the epithet “dialectical” can hardly be withheld – the emphasis upon historical development, opposition between contraries, is surely just as a characteristic of constructivism as of dialectic, and that the idea of wholeness figures centrally in structuralism as in dialectical modes of thought is obvious. (p.121)

What is the dialectical reason for Levi-Strauss? It is always constitutive, in the sense of being venturesome, building bridges and crossing them, whereas analytical reason separates because it wants not only to understand but to control (122)

Marx and structuralism: there is a structuralist strand in Marx, something halfway between what we called global and analytical structuralism, since he distinguishes “real infrastructures” from “ideological infrastructures” and describes the former in terms which, though remaining qualitative, are precise enough to bring us close to directly observable relations (p.125)